From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is:

Step-by-step solution

The dimensional formulae of aligned & e = [ M ^0 ~L ^0 ~T ^1 ~A ^1 ] & ₀= [ M ⁻¹ ~L ^3 ~T ^4 ~A ^2 ] & G = [ M ⁻¹ ~L ^3 ~T ⁻² ] & and m _ e = [ M ^1 ~L ^0 ~T ^0 ] & Now, e ^2 2 ₀ Gm _ e ^2 &= [ M ^0 ~L ^0 ~T ^1 ~A ^1 ]^2 2 [ M ⁻¹ ~L ⁻³ ~T ^4 ~A ^2 ] [ M ⁻¹ ~L ^3 ~T ⁻² ] [ M ^1 ~L ^0 ~T ^0 ]^2 aligned aligned &= [ T ^2 ~A ^2 ] 2 [ M ⁻¹⁻¹⁺² ~L ⁻³⁺³ ~T ⁴⁻² ~A ^2 ] &= [ T ^2 ~A ^2 ] 2 [ M ^0 ~L ^0 ~T ^2 ~A ^2 ] = 1 2 aligned 1 2 is dimensionless thus the combination e ^2 2 ₀ Gm _ e ^2 would have the same value in diffe